Advances in Continuum Mechanics and Thermodynamics of Material Behavior, 2000
We use a mixed 3-dimensional variational principle to derive 2-dimensional equations for an aniso... more We use a mixed 3-dimensional variational principle to derive 2-dimensional equations for an anisotropic plate-like piezoelectric body and one-dimensional equations for an anisotropic beam-like piezoelectric body. The formulation accounts for double forces without moments which may change the thickness of the plate and deform the cross-section of the rod. The dependence of the bending rigidities of a transversely isotropic plate upon the angle between the normal to the midsurface and the direction of transverse isotropy is exhibited. The plate equations are used to study the cylindrical deformations of a transversely isotropic plate due to equal and opposite charges applied to its top and bottom surfaces. It is also found that a piezoelectric circular rod with axis of transverse isotropy not coincident with its centroidal axis and subjected to electric charges at the end faces is deformed into a non-prismatic body.
International Journal of Solids and Structures, 2005
The design of an inductance/capacitance two-terminal distributed passive electric network for sim... more The design of an inductance/capacitance two-terminal distributed passive electric network for simultaneously controlling several flexural modes of vibration is discussed. The efficiency of the network to annul multimode vibrations of simply supported, clamped-clamped and cantilever beams is demonstrated.
A variational formulation is proposed for a family of elastic-plastic-damage models within the fr... more A variational formulation is proposed for a family of elastic-plastic-damage models within the framework of rate-independent materials. That consists first in defining the total energy which contains, in particular, a gradient damage term and a term which represents the plastic dissipation but depends also on damage. Then, the evolution law is deduced from the principles of irreversibility, stability and energy balance. Accordingly, the plastic dissipation term which appears both in the damage criterion and the plastic yield criterion plays an essential role in the damage-plasticity coupling. Suitable constitutive choices on how the plastic yield stress decreases with damage, allows us to obtain a rich variety of coupled responses. A particular attention is paid on the equations which govern the formation of cohesive cracks where the displacement is discontinuous and the plasticity localizes. In the one-dimensional traction test where the solution is obtained in a closed form, we show that, because of damage localization, a cohesive crack really appears at the center of the damage zone before the rupture and the associated cohesive law is obtained in closed form in terms of the constitutive parameters. A Finite Element discrete version of the energy functional is used to simulate a two-dimensional traction test over a rectangular domain with mixed boundary conditions; again a localized band of plastic strain is generated seemingly independent of the mesh size.
CISM International Centre for Mechanical Sciences, 2008
The small sensitivity to local variations of mechanical characteristics turns out to be the major... more The small sensitivity to local variations of mechanical characteristics turns out to be the major limit of indirect identification techniques based on frequency response measurements. To overcome this limit, the use of sensitivity enhancement techniques has recently proposed: the monitored structure is coupled to an auxiliary system, the constitutive parameters of which are then suitably tuned to enhance the sensitivities relevant to the identification process. The damage identification problem in these “augmented” structures is here introduced, and its main advantages and drawbacks are discussed. A beam-like structure coupled to a network of piezoelectric patches supplies an enlightening application of the proposed technique.
This paper studies the stable equilibrium shapes of free multilayered orthotropic plates loaded b... more This paper studies the stable equilibrium shapes of free multilayered orthotropic plates loaded by inelastic deformations induced by thermal and piezoelectric effects. Starting with a Von Kármán plate kinematics and an energetic formulation, a discrete intrinsic nonlinear model in terms of curvatures only is deduced. The model has 3 degrees of freedom, namely the components of the symmetric curvature tensor, which is supposed to be uniform in space. Despite of this rough assumption, the analytical results about the equilibrium shapes and their stability show a good agreement with the finite element simulations performed with a commercial code. Literature results about the bistable behavior of isotropic plates under a single-parameter loading are extended to the orthotropic case with two loading parameters. In light of a global stability analysis and a phase portrait as a function of the inelastic curvatures, we study possible actuation techniques for controlling the transition of the plate between its two stable configurations. We show that with a suitable two-parameter actuation, it is possible to get a controlled quasi-static transition, avoiding any instability phenomenon. Numerical simulations on a realistic case study support the technological feasibility of the proposed actuation technique when using active piezoelectric layers to control the inelastic curvature.
Advances in Continuum Mechanics and Thermodynamics of Material Behavior, 2000
We use a mixed 3-dimensional variational principle to derive 2-dimensional equations for an aniso... more We use a mixed 3-dimensional variational principle to derive 2-dimensional equations for an anisotropic plate-like piezoelectric body and one-dimensional equations for an anisotropic beam-like piezoelectric body. The formulation accounts for double forces without moments which may change the thickness of the plate and deform the cross-section of the rod. The dependence of the bending rigidities of a transversely isotropic plate upon the angle between the normal to the midsurface and the direction of transverse isotropy is exhibited. The plate equations are used to study the cylindrical deformations of a transversely isotropic plate due to equal and opposite charges applied to its top and bottom surfaces. It is also found that a piezoelectric circular rod with axis of transverse isotropy not coincident with its centroidal axis and subjected to electric charges at the end faces is deformed into a non-prismatic body.
International Journal of Solids and Structures, 2005
The design of an inductance/capacitance two-terminal distributed passive electric network for sim... more The design of an inductance/capacitance two-terminal distributed passive electric network for simultaneously controlling several flexural modes of vibration is discussed. The efficiency of the network to annul multimode vibrations of simply supported, clamped-clamped and cantilever beams is demonstrated.
A variational formulation is proposed for a family of elastic-plastic-damage models within the fr... more A variational formulation is proposed for a family of elastic-plastic-damage models within the framework of rate-independent materials. That consists first in defining the total energy which contains, in particular, a gradient damage term and a term which represents the plastic dissipation but depends also on damage. Then, the evolution law is deduced from the principles of irreversibility, stability and energy balance. Accordingly, the plastic dissipation term which appears both in the damage criterion and the plastic yield criterion plays an essential role in the damage-plasticity coupling. Suitable constitutive choices on how the plastic yield stress decreases with damage, allows us to obtain a rich variety of coupled responses. A particular attention is paid on the equations which govern the formation of cohesive cracks where the displacement is discontinuous and the plasticity localizes. In the one-dimensional traction test where the solution is obtained in a closed form, we show that, because of damage localization, a cohesive crack really appears at the center of the damage zone before the rupture and the associated cohesive law is obtained in closed form in terms of the constitutive parameters. A Finite Element discrete version of the energy functional is used to simulate a two-dimensional traction test over a rectangular domain with mixed boundary conditions; again a localized band of plastic strain is generated seemingly independent of the mesh size.
CISM International Centre for Mechanical Sciences, 2008
The small sensitivity to local variations of mechanical characteristics turns out to be the major... more The small sensitivity to local variations of mechanical characteristics turns out to be the major limit of indirect identification techniques based on frequency response measurements. To overcome this limit, the use of sensitivity enhancement techniques has recently proposed: the monitored structure is coupled to an auxiliary system, the constitutive parameters of which are then suitably tuned to enhance the sensitivities relevant to the identification process. The damage identification problem in these “augmented” structures is here introduced, and its main advantages and drawbacks are discussed. A beam-like structure coupled to a network of piezoelectric patches supplies an enlightening application of the proposed technique.
This paper studies the stable equilibrium shapes of free multilayered orthotropic plates loaded b... more This paper studies the stable equilibrium shapes of free multilayered orthotropic plates loaded by inelastic deformations induced by thermal and piezoelectric effects. Starting with a Von Kármán plate kinematics and an energetic formulation, a discrete intrinsic nonlinear model in terms of curvatures only is deduced. The model has 3 degrees of freedom, namely the components of the symmetric curvature tensor, which is supposed to be uniform in space. Despite of this rough assumption, the analytical results about the equilibrium shapes and their stability show a good agreement with the finite element simulations performed with a commercial code. Literature results about the bistable behavior of isotropic plates under a single-parameter loading are extended to the orthotropic case with two loading parameters. In light of a global stability analysis and a phase portrait as a function of the inelastic curvatures, we study possible actuation techniques for controlling the transition of the plate between its two stable configurations. We show that with a suitable two-parameter actuation, it is possible to get a controlled quasi-static transition, avoiding any instability phenomenon. Numerical simulations on a realistic case study support the technological feasibility of the proposed actuation technique when using active piezoelectric layers to control the inelastic curvature.
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Papers by Stefano Vidoli